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Numbers k such that 12 divides prime(1) + ... + prime(k).
11

%I #8 May 14 2024 03:58:39

%S 97,99,103,105,107,111,119,121,125,129,161,163,169,175,177,179,185,

%T 195,199,203,205,207,211,213,233,235,237,273,305,307,309,311,329,335,

%U 337,343,345,347,353,357,421,423,425,439,443,445,447,449,455,463,511,513,515,539

%N Numbers k such that 12 divides prime(1) + ... + prime(k).

%H Amiram Eldar, <a href="/A111326/b111326.txt">Table of n, a(n) for n = 1..10000</a>

%t Position[Accumulate[Prime[Range[400]]], _?(Divisible[#, 12] &)] // Flatten (* _Amiram Eldar_, May 14 2024 *)

%o (PARI) lista(pmax) = {my(s = 0, k = 0); forprime(p = 2, pmax, k++; s += p; if(!(s % 12), print1(k, ", ")));} \\ _Amiram Eldar_, May 14 2024

%Y Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111323, A111324, A111325, A111327.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 05 2005